Improved numerical modelling of clusters of galaxies

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Abstract
We have attempted to model the formation and evolution of clusters of galaxies consisting of both galaxy and dark background particles. Starting from initial conditions with only equal-mass dark particles, as traditionally done, at a certain epoch galaxies are identified using a local density percolation technique combined with a virial equilibrium condition. For each galaxy found, its constituent particles are replaced by a single softened particle, where the binding energy of the original particles is transferred into internal energy of the single particle galaxy. While rather crude, this is a first attempt to include dissipation (by hand) on galactic scales in inherently dissipationless N-body methods. More importantly, it keeps galaxies intact which would otherwise get disrupted within clusters because of either two-body or tidal effects. Not doing so results in smooth final mass distributions, in which galaxies cannot be identified, even for quite large particle numbers. The softening parameter of a galaxy is proportional to the half-mass radius of its original group, so a spectrum of masses and sizes is thus produced automatically. However, the softening of the dark background particles is still chosen on numerical grounds, since at present their nature and distribution are largely unknown. These ideas have been tested on several matter distributions, including an average piece of universe, a small cluster (or group) of galaxies with a mass of around 2×1014 M⊙, regular clusters with a mass of almost 1015 M⊙, and a rich cluster heavier than 3 × 1015 M⊙. Galaxies are made 'instantly' at one or more redshifts, supposing a peak in the galaxy formation rate, with both a lower and an upper mass cut-off. The resulting mass functions compare reasonably to observed luminosity functions. Mass segregation of the galaxies with respect to the dark matter is shown to occur, with details depending on the epoch of galaxy formation. A clear spatial bias between these two mass components is observed. There is only marginal evidence for velocity bias in some of the simulations. The segregation and biasing effects cause a general underestimation of the total cluster mass. H0=50 km s-1Mpc-1 is adopted throughout the paper.

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